1. Field of the Invention
The present invention relates to technologies for the simulation of a semiconductor process including oxidation and film formation, and particularly, to a method of the simulation of a topography for a geometrical change of a material region, a simulator for realizing the simulation method and a program for accomplishing the simulation method.
2. Description of the Related Art
In a topography simulation for calculating the topography of a semiconductor device in an oxidation, deposition and etching step or the like, a string model showing the topography of a semiconductor device as shown in FIG. 1A is usually used. In the string model, the topography of a semiconductor is shown by a string of a line segment Si connecting a boundary point Pi and a boundary point Pi+1 and each boundary point P is moved in conformity with each process model at each small time interval to calculate the hourly variation in device topography.
Also, as shown in FIG. 1B, a mesh provided with plurally divided triangle elements Ei is disposed in the region enclosed by a string to calculate oxidation and impurity profiles. The boundary point Pi and a point Ni+1 within the region are called a node N. In the case where the mesh exists in the region, all nodes N including not only the boundary point but also points within the region are moved at each small time interval to calculate the hourly variation in the topography of a semiconductor device. A topography simulation method using such a string model is disclosed in, for example, “VLSI TECHNOLOGY, S.M. Sze, McGraw-Hill, (1988)”. However, the prior technologies have the problems shown below.
FIG. 2 shows a flowchart of a conventional method for controlling the length of a line segment s. First, in a step S61, the number nloop of steps as to what times the calculation of the displacement is looped is set to a required number and the present number j of steps is set to zero. Next, in a step S62, 1 is added to the present number j of steps. In a step S63, the component of all boundary points P as to the displacement is calculated, and in a step S64, all boundary points P are moved. In a step S65, the length of at least one or more line segments s constituting a string is regulated. The aforementioned steps S61–S65 are repeated until the present number j of steps is equal to nloop.
FIG. 3 is a flow chart showing an internal flow of adding boundary point P to regulate the length of the line segment s in the step S65 of FIG. 2. First, in a step S71, the length of the line segment s after all boundary points P are moved. Next, in a step S72, the identification number i of the line segment s is set to 1. In a step S73, whether or not the length r1 of the line segment s1 after the boundary point P is moved is greater than a maximum length lmax to be specified is judged. If r1≧lmax, a new boundary point P is added to the line segment s1 in a step S74. In a step S75, 1 is added to the number i. In a step S76, whether or not the number i is smaller than the number obtained by adding 1 to a maximum identification number (m−1) is judged. If it is judged to be smaller, the flow is returned to the step S73 and these steps S73–S75 are repeated until the identification number i is equal to m. If the identification number i is equal to m, the process is finished. Namely, all line segments s were judged in order of the number i as to whether or not the length r is greater than the maximum length lmax. If the length r of the line segment s is larger than the maximum length lmax, a new boundary point P is added to the line segment s.
FIG. 4 is a flow chart showing an internal flow to eliminate a boundary point P to thereby regulate the length of the line segment s in the step S65 of FIG. 2. First, in a step S81, the length of all line segments s after the boundary point P is moved is calculated. Next, in a step S82, the identification number i of the line segment s is set to 1. In a step S83, whether or not the rength r1 of the line segment s1 after the boundary point P is moved is smaller than a minimum length lmin to be specified is judged. If r1≦lmin, in a step S84, one of the boundary points P constituting the line segment s is eliminated and a new line segment s′1 is produced. In a step S85 and a step S86, when the eliminated boundary P is a connecting point between the line segments s1, and s2, s2 is designated as s′1. These steps are repeated until the identification number i is equal to m−1.
However, if the length r of the line segment s is set to the maximum length lmax to be specified or more, a new boundary point is always added to the line segment, giving rise to the problem that useless boundary points are increased. For example, when a groove 59 is formed on a silicon substrate 52 as shown in FIG. 5A, a silicon oxide film 61 is formed on the surface of the silicon substrate 52 by deposition as shown in FIG. 5B. The result of topography simulation as to a region 60 is shown FIG. 6. As shown in FIG. 6, the surface string of the substrate 52 is constituted of line segments arranged at unequal intervals. Each topography between boundary points P0 and P1 and between boundary points P15 and P16 is considered to be able to be estimated from each displacement between the boundary points P0 and P1 and between the boundary points P15 and P16 respectively and no node is arranged between the boundary points P0 and P1 and between the boundary points P15 and P16, whereby it is expected to shorten calculation time. However, because the value of the specified maximum length lmax is short, there is the case where needless boundary points 62 and 64 are prepared and therefore the calculation time cannot be shortened as is expected.
On the other hand, it is effective to dispose a new node 63 on lengthened line segments s13 and s14 having lengths of r13 and r14 respectively to raise the accuracy of topography simulation. However, because the specified maximum length lmax may be larger, the node 63 is formed on the line segment s14 but no node is produced on the line segment s13 and therefore the accuracy of the topography cannot be raised.
In this manner, the value of an absolute maximum length lmax which shortens time and improves accuracy does not exist, causing such an inconvenience that customers must design an optimum value of each of the maximum length lmax and minimum length lmin of the line segment s from the structure of a semiconductor which must be analyzed by the customers. Specifically, the conventional topography processing methods involve the case where exact topography of a device cannot be expressed and the case where calculation is made in vain. Therefore, it cannot be said that these method are practical to develop semiconductor devices.